A179692 Numbers of the form p^9*q where p and q are distinct primes.

1536, 2560, 3584, 5632, 6656, 8704, 9728, 11776, 14848, 15872, 18944, 20992, 22016, 24064, 27136, 30208, 31232, 34304, 36352, 37376, 39366, 40448, 42496, 45568, 49664, 51712, 52736, 54784, 55808, 57856, 65024, 67072, 70144, 71168, 76288, 77312, 80384, 83456

Offset

1,1

Links

T. D. Noe, Table of n, a(n) for n = 1..1000

Will Nicholes, Prime Signatures

Mathematica

f[n_]:=Sort[Last/@FactorInteger[n]]=={1, 9}; Select[Range[90000], f]

Prog

(PARI) list(lim)=my(v=List(), t); forprime(p=2, (lim\2)^(1/9), t=p^9; forprime(q=2, lim\t, if(p==q, next); listput(v, t*q))); vecsort(Vec(v)) \\ Charles R Greathouse IV, Jul 24 2011
(Python)
from sympy import primepi, integer_nthroot, primerange
def A179692(n):
    def bisection(f, kmin=0, kmax=1):
        while f(kmax) > kmax: kmax <<= 1
        kmin = kmax >> 1
        while kmax-kmin > 1:
            kmid = kmax+kmin>>1
            if f(kmid) <= kmid:
                kmax = kmid
            else:
                kmin = kmid
        return kmax
    def f(x): return n+x-sum(primepi(x//p**9) for p in primerange(integer_nthroot(x, 9)[0]+1))+primepi(integer_nthroot(x, 10)[0])
    return bisection(f, n, n) # Chai Wah Wu, Feb 21 2025

Crossrefs

Cf. A006881, A007304, A065036, A085986, A085987, A092759, A178739, A179642, A179643, A179644, A179645, A179646, A179664, A179665, A179666, A179667, A179668, A179669, A179670, A179671, A179672, A179688, A179689, A179690, A179691.

Sequence in context: A088362 A045123 A252419 * A105923 A229507 A203981

Adjacent sequences: A179689 A179690 A179691 * A179693 A179694 A179695

Keyword

nonn,changed

Author

Vladimir Joseph Stephan Orlovsky, Jul 24 2010

Status

approved